The day before a long, holiday break requires careful planning if you actually want to get something meaningful accomplished. I try to seize these times as opportunities to show students something mathematically new and novel. Typically, this time of year, that means introducing students to the world of fractals. Most middle schoolers I’ve worked with have never heard of fractals, yet the familiar concepts of patterns, repetition and similarity are effectively reinforced through some fun “fractivities”.
With only 40-ish minute class periods, I spend two days on fractals. Day 1 is spent generating Sierpinski’s Triangle in 2-D using this template. It’s fun to watch students become nearly addicted to the task! This year in particular, I had students create the most intricate and detailed fractals I’ve seen on paper! One student proudly boasted to me today that he “only” spent 4 hours on it at home last evening!
Day 2 we graduate to 3-D cutout fractal pop-up cards which, ironically, can look quite like a Christmas tree! Students stare in amazement when I show them various samples I’ve created, and I challenge them to create as many “iterations” as they physically can, since the paper becomes quite thick after a few folds. These are a big hit due to their complex appearance, yet the task is quite feasible. Having a document camera in my classroom is a lifesaver for demonstrations like this! Students are also quick to help one another, and the finished product evokes excitement and pride from all.
When I see such joy, curiosity and motivation from students, I wonder if we have this whole math education thing all wrong. Students seem to be starving to learn something new! Yet, there are topics we teach over and over again, year after year, and students just don’t seem to master them (take fractions, for example… even my top students this year initially added fractions by adding numerators, then adding denominators… DOH!) How can I better “grab” students’ attention for topics they “need” to know, yet tap into that curiosity, motivation, and passion that surfaces when students see something new, like fractals? Is it possible to reach students this way on a daily basis? I’d like to hope so – it’s what I strive to do. (I don’t always succeed though!)
An aside that relates… the other day while wrapping up several lessons on simplest radical form, an 8th-grader declared, in the middle of class, loud enough for all her peers to hear her: “I am thoroughly enjoying math class right now. It is so weird.” The spirit of her statement speaks volumes. These algebra students have seen some topics over and over again for years, but THIS topic was brand new – they had to learn the concept from scratch. Sure, there were plenty of growing pains along the way… and whining… yet in the end, when the “light bulbs” turned on, students still recognized the joy of learning. And that, my friends, is what it’s all about.
Back to my original topic – if you try some “fractivities” let me know how you liked them! The Fractal Foundation website is a great resource!